Question: Solve for $x$ and $y$ using elimination. ${-3x-4y = -19}$ ${3x+5y = 20}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3x$ and $3x$ cancel out. ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {-3x-4y = -19}\thinspace$ to find $x$ ${-3x - 4}{(1)}{= -19}$ $-3x-4 = -19$ $-3x-4{+4} = -19{+4}$ $-3x = -15$ $\dfrac{-3x}{{-3}} = \dfrac{-15}{{-3}}$ ${x = 5}$ You can also plug ${y = 1}$ into $\thinspace {3x+5y = 20}\thinspace$ and get the same answer for $x$ : ${3x + 5}{(1)}{= 20}$ ${x = 5}$